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x-2-\frac{1}{2}x=-2
Subtract \frac{1}{2}x from both sides.
\frac{1}{2}x-2=-2
Combine x and -\frac{1}{2}x to get \frac{1}{2}x.
\frac{1}{2}x=-2+2
Add 2 to both sides.
\frac{1}{2}x=0
Add -2 and 2 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since \frac{1}{2} is not equal to 0, x must be equal to 0.